Question

In a cyclic quadrilateral ABCD if angle a -angle c =60°then prove that the smaller of two angle is 60°

Answer 1

Hi,

Here's ur answer :-

There is a rule that the sum of opposite angles in a cyclic quadrilateral is always 180 degree.

Therefore, As in quadrilateral. ABCD, A and C are opposite angles, their sum would be 180 degree.

So, Let the smaller angle. (C) be x and the bigger angle be 180-x

180-x - x = 60
=> 180-2x = 60
=> 2x = 180-60=120
=> x= 60

So, the smaller angle is 60 and bigger angle is 180.

HOPE IT HELPS (^_^)

Answer 2

Answer :

WE have,

∠A - ∠C = 60° ...... (i)

Since, ABCD is a cyclic quadrilateral

Then,

∠A + ∠C = 180°....... (ii)

Adding (i) and (ii), we get

∠A - ∠C + ∠A + ∠C = 60° + 180°

2 ∠A = 240°

∠A = 120°

Put value of ∠A in (ii), we get

120° + ∠C = 180°

∠C = 60°